Gradient of func. If None, then either func must return the
function value and the gradient (f,g=func(x,*args))
or approx_grad must be True.

args : tuple

Arguments to pass to function.

approx_grad : bool

If true, approximate the gradient numerically.

bounds : list

(min, max) pairs for each element in x0, defining the
bounds on that parameter. Use None or +/-inf for one of
min or max when there is no bound in that direction.

epsilon : float

Used if approx_grad is True. The stepsize in a finite
difference approximation for fprime.

scale : list of floats

Scaling factors to apply to each variable. If None, the
factors are up-low for interval bounded variables and
1+|x] fo the others. Defaults to None

offset : float

Value to substract from each variable. If None, the
offsets are (up+low)/2 for interval bounded variables
and x for the others.

messages : :

Bit mask used to select messages display during
minimization values defined in the MSGS dict. Defaults to
MGS_ALL.

disp : int

Integer interface to messages. 0 = no message, 5 = all messages

maxCGit : int

Maximum number of hessian*vector evaluations per main
iteration. If maxCGit == 0, the direction chosen is
-gradient if maxCGit < 0, maxCGit is set to
max(1,min(50,n/2)). Defaults to -1.

maxfun : int

Maximum number of function evaluation. if None, maxfun is
set to max(100, 10*len(x0)). Defaults to None.

eta : float

Severity of the line search. if < 0 or > 1, set to 0.25.
Defaults to -1.

stepmx : float

Maximum step for the line search. May be increased during
call. If too small, it will be set to 10.0. Defaults to 0.

accuracy : float

Relative precision for finite difference calculations. If
<= machine_precision, set to sqrt(machine_precision).
Defaults to 0.

fmin : float

Minimum function value estimate. Defaults to 0.

ftol : float

Precision goal for the value of f in the stoping criterion.
If ftol < 0.0, ftol is set to 0.0 defaults to -1.

xtol : float

Precision goal for the value of x in the stopping
criterion (after applying x scaling factors). If xtol <
0.0, xtol is set to sqrt(machine_precision). Defaults to
-1.

pgtol : float

Precision goal for the value of the projected gradient in
the stopping criterion (after applying x scaling factors).
If pgtol < 0.0, pgtol is set to 1e-2 * sqrt(accuracy).
Setting it to 0.0 is not recommended. Defaults to -1.

rescale : float

Scaling factor (in log10) used to trigger f value
rescaling. If 0, rescale at each iteration. If a large
value, never rescale. If < 0, rescale is set to 1.3.

callback : callable, optional

Called after each iteration, as callback(xk), where xk is the
current parameter vector.

Interface to minimization algorithms for multivariate functions. See the ‘TNC’ method in particular.

Notes

The underlying algorithm is truncated Newton, also called
Newton Conjugate-Gradient. This method differs from
scipy.optimize.fmin_ncg in that

It wraps a C implementation of the algorithm

It allows each variable to be given an upper and lower bound.

The algorithm incoporates the bound constraints by determining
the descent direction as in an unconstrained truncated Newton,
but never taking a step-size large enough to leave the space
of feasible x’s. The algorithm keeps track of a set of
currently active constraints, and ignores them when computing
the minimum allowable step size. (The x’s associated with the
active constraint are kept fixed.) If the maximum allowable
step size is zero then a new constraint is added. At the end
of each iteration one of the constraints may be deemed no
longer active and removed. A constraint is considered
no longer active is if it is currently active
but the gradient for that variable points inward from the
constraint. The specific constraint removed is the one
associated with the variable of largest index whose
constraint is no longer active.